Thermal effects of fire on a nearby fuel storage tank

Journal of Loss Prevention in the Process Industries 62 (2019) 103990

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Thermal effects of fire on a nearby fuel storage tank Susana N. Espinosa a, Rossana C. Jaca a, Luis A. Godoy b, * a b

Facultad de Ingeniería, Universidad Nacional del Comahue, Buenos Aires 1400, Neuqu�en, Argentina Instituto de Estudios Avanzados en Ingeniería y Tecnología, IDIT, CONICET/Universidad Nacional de C� ordoba, C� ordoba, Argentina

A R T I C L E I N F O

A B S T R A C T

Keywords: Combustible fuels Fire Finite element modeling Heat transfer Steel tanks

This work presents numerical modeling and quantitative results of the heat transfer process from a burning tank to an adjacent tank. The flame is represented by a solid flame model in which two zones are identified: a lower clear flame layer with high temperatures and a darker upper layer in which the flame carries soot and smoke. Semi-empirical models are used to estimate the geometry of the flame; other models were also adopted to ac­ count for wind effects. The emissive power of each layer of the flame was locally evaluated as a function of temperature. A heat transfer process was followed from the flame to the target tank, at which an energy balance is carried out to include radiation from the flame, radiation from target tank surfaces, and convection to air and to fuel stored in the target tank. The results are presented in the form of temperature distributions on the target tank, which are an ingredient to perform structural analysis. Parametric studies are carried out to investigate the influence of the vertical location of the flame, wind speed, level and temperature of the fuel stored in the target tank, size and distance between tanks. Flame location at ground level, wind speed, higher temperatures of stored fluids, and short separation between tanks are identified as crucial elements increasing thermal effects on the target tank, but the results are not so much influenced by tank size.

1. Introduction The available evidence of accidents in fuel and oil production facil­ ities indicates that fire and explosions are the most frequent causes of tank failure (Chang and Lin, 2006). Fire accidents may affect a single tank, whereas in other cases an initial failure is part of a domino effect, in which fire propagates from one tank to another (Landucci et al., 2009; Reniers and Cozzani, 2013). Dramatic illustrations of such accidents in the XXI Century occurred in the island of Guam in the Pacific Ocean in 2002, followed by two notorious cases in 2005: Some 20 tanks were destroyed by fire in Buncefield, UK (Buncefield, 2008), and 50 tanks in Texas City, USA. A fire with similar consequences occurred in Bayamon, Puerto Rico, in 2009, in which more than 20 tanks were destroyed (Batista-Abreu and Godoy, 2011, Batista-Abreu and Godoy, 2013; Godoy and Batista-Abreu, 2012). Other smaller and less publicized cases occurred in Gibraltar in 2011; Amuay, Venezuela, in 2012; Río de Janeiro, Brazil, in 2013; Malargüe, Argentina, in 2014; and the list would be considerably increased if cases in Asia were included (see, for example, Mishra et al., 2013). In view of the urgent need to account for fire as part of accident investigations and at a design stage, it is surprising to find that research

effort has been placed only recently to elucidate the consequences of fire in tank farms. Interest in this field of research is largely motivated by the need to establish safe distances between tanks, in order to reduce the possibility of fire propagation between tanks; this is addressed at present in codes such as those developed by the National Fire Protection Asso­ ciation (NFPA 30, 2012), American Petroleum Institute (API 650, 2010) and the US Environmental Protection Agency (EPA-UST, 2015). Modeling this problem requires drawing attention to an adequate representation of the source of fire, the heat transfer process from the fire source to the target structure, and the heat balance at the target structure including the fluid stored and the environment. The outcome of such study is the temperature distribution on the target structure, and this is the starting point to model the mechanical behavior of the target structure. This paper addresses the thermal modeling from fire source to target structure, whereas the structural response is investigated elsewhere. Consider first the source of fire. Based on observations from real events, it is commonly assumed that fire in a tank farm originates in a tank, which is subsequently identified as the source tank. Burning of fuel in this tank causes a flame that radiates heat until it reaches a second tank, known as the target tank. One of the better-known families of fire

* Corresponding author. E-mail addresses: [email protected] (S.N. Espinosa), [email protected] (R.C. Jaca), [email protected] (L.A. Godoy). https://doi.org/10.1016/j.jlp.2019.103990 Received 17 April 2019; Received in revised form 2 October 2019; Accepted 22 October 2019 Available online 30 October 2019 0950-4230/© 2019 Elsevier Ltd. All rights reserved.

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

models at the heat source is known as the Pool-Fire Model, which de­ scribes a flame with turbulent diffusion. The process is characterized by buoyancy-driven natural convection and burning on top of a pool with vaporized fuel having a negligible initial moment (Rew et al., 1997). Estimation of the emissive power of a flame is normally carried out by considering that heat radiates from the center of a flame (an approach known as “point source model”) or from the surface of a solid cylinder (which is known as “solid flame model”). The solid flame model may include one or two different zones of radiation. Pool-fire models have been employed in the technical literature for at least 20 years. Rew et al. (1997) developed a semi-empirical model known as Poolfire6, based on a solid flame representation and full-scale data, and produced a data base of properties including burning speed of fuel, emissive power of fuels, ranging from liquefied natural gas and liquefied oil gas to heavy hydrocarbon, gasoline, diesel, and methanol. This database has been used by other investigators to estimate properties that are required in simulations. McGrattan et al. (2000) presented a methodology to evaluate radiation emitted from large pool fires using a point-source model. Large scale pool-fires were reviewed by Steinhaus et al. (2007), who analyzed the burning of fuels, soot production, radi­ ation emission, fire distribution, and other related topics. Wind increases the risk of fire propagation because the efficiency of combustion is improved by a higher intake of oxygen in air; further, the inclination and extension of the flame are severely modified in the presence of wind. Sengupta et al. (2011) improved the point-source model to account for wind effects on the flame height and fire distribution, and estimated the safe distances between tanks containing volatile or inflammable fluids. Regarding heat exchange, the main effect is radiation from a fire source to a target tank; however, convection and internal radiation are crucial as heat reaches the target tank. To model this process, accurate estimates of convection coefficients should be made because these are not constant properties but strongly depend on temperature, on stored fluid properties, and on the properties of the surface of the target structure. There are two main areas of interest that may motivate the detail thermal analysis occurred from a source of fire to a target tank: On the one side, Chemical Engineers are more concerned with the possibility of burning of fuels stored in a target tank in order to estimate fire propa­ gation from one tank to another. The subject of domino effects has been discussed by a number of authors and has been summarized in the book edited by Reniers and Cozzani (2013). On the other side, Structural Engineers are concerned with understanding the influence of different effects on the temperature reaching the surface of the target tank in order to proceed with studies on the mechanics of stress and stability response, i.e. buckling and/or material failure of the metal shell. This work reports research that is motivated by the Structural Engineering perspective. Liu and coworkers were perhaps the first to present a detailed study of the heat process from the source to a target structure (Liu, 2011; Liu et al., 2012). Within the context of a pool-fire model, they adopted a fixed flame geometry and a fixed temperature and assumed an average value of emissive power for the complete flame surface. Because the emissive power of fire was not modeled, parametric studies were per­ formed to illustrate its influence on temperature profiles. Wind speed was not taken into account. Average air and fuel film coefficients were used in the calculations at the target tank. The model served as a basis to perform extensive parametric studies in terms of flame height and po­ sition, target tank diameter, and level of fluid stored in the target tank. The implementation of the heat transfer model was carried out using the general-purpose program ABAQUS. Liu (2011) did not include the ge­ ometry of the flame and its radiation as part of her modeling and instead adopted two flame heights, namely one and two times the diameter of a tank, and assumed an average flame temperature of 900 � C. Da Silva Santos and Landesmann (2014) improved the flame model by estimating the flame geometry using semi-empirical models available in the literature. A transient model was used to obtain temperatures on

the target tank, considering a single emissive power for the complete flame surface. Wind velocities of 5 m/s were also taken into account in the model. These authors addressed the minimum safe distances be­ tween tanks containing gasoline or ethanol by assuming flames radiating from the top of the source tank. Internal radiation was not considered in the target tank, and low values of liquid film coefficient were assumed. The same convection coefficients were used to model two different products, gasoline and ethanol. These authors considered temperature evolution as a function of fire elapsed time and investigated tanks made of steel and of concrete (a unique study in this field). Espinosa et al. (2018) followed a heat transfer approach to evaluate temperatures reaching the target tank, in which the natural convection from the metal tank to the fluid stored was modeled by Computational Fluid Dynamics (CFD) using co-simulation within ABAQUS. Velocity, pressure and temperature fields in the fuel and on the surface of the steel shell were obtained simultaneously. The studies by Pantousa (2018) emphasized vertical as well as circumferential variations of temperatures at a target tank considering multiple fire scenarios. Modeling was based on the solid flame model and assuming one zone within the flame, while burning was considered from the top of the tank at the source. The assumed parameters of wind velocity and emissive power of the flame were the same as in da Silva-Santos and Landesmann (2014). One key aspect in the study of Pantousa was consideration that several tanks were burning simulta­ neously and radiating to a target tank; an upper bound in temperatures was reached for two or three heat sources, depending on other condi­ tions. Temperature evolution in time was accounted for by means of a transient study. In order to fully understand the structural behavior, and estimate damage and collapse of oil infrastructure under an adjacent fire, as well as to refine the way by which such facilities are designed, it is crucial to improve our modeling capabilities and to identify the parameters that play a significant role in the temperature distribution on the target tank. This problem is addressed in this paper by attempting to refine some of the assumptions made in the literature. The main premises of this work are (a) The temperature distribution should be obtained by an energy balance considering all modes of heat transfer; (b) The air and fuel convection coefficients should be estimated as a function of their thermo-physical properties and wind velocities; (c) Because the film coefficients are a function of temperature, their values should be updated during the heat transfer process. This work examines the effects of tank geometry, tanks location, fuel level, and environmental condi­ tions by means of a heat transfer model embedded into the computa­ tional model. 2. Flame model Consider the simplest case of a tank farm in which fire initiated in a source tank and interest focuses on the heat effects that take place in a target tank. The net heat flow from the source of fire to the target structure depends on the type of fuel stored in the tanks, flame location, wind velocity and direction, time of duration of fire, distance between source and target tanks, constitutive material of tank walls, tank ge­ ometry and others. As illustrated in Fig. 1, flame location is another relevant parameter in this problem. There is ample evidence that there are cases (known as pool fire) in which the flame emerges from the top of the source tank (as shown in Fig. 1.a); whereas in other cases (known as full surface fire) the flame starts at the top and extends by cracks or oil spills down to the bottom of the tank, as shown in the case of Fig. 1.b. Industrial accidents caused by lightning on a tank may induce either pool fire or full surface fire (Necci et al., 2014). Reports from real accidents and from experiments in laboratory conditions (Considine, 1984; McGrattan et al., 2000; Beyler, 2002; Mansour, 2012) show that the type of flame strongly depends on the fuel that burns. The combustion of liquefied gases leads to a clear flame (without the presence of smoke), whereas combustion of hydrocarbon 2

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

Fig. 1. Examples of flame location in the source tank: (a) Flame emerging from roof level, (b) Flame reaching ground level. Both figures were taken from the same accident in Gibraltar, May 31, 2011. Web reference for Fig. 1: https://commons.wikimedia.org/wiki/File:Oil_sullage_tank_burns_after_explosion.jpg, http://www. dailymail.co.uk/news/article-1393024/Gibraltar-harbour-explosion-injures-12-oil-tank-blows-welding-work.html.

fluids yields two well-defined zones within a flame: A lower region with clear flame and a darker upper region characterized by dense smoke and soot particles, with parts of heat flames emerging intermittently. Empirical models have been developed for each type of flame. Single layer models consider an average emissive power for the complete flame surface; such models are adequate to represent burning of liquefied gases. Two-layer models (see, for example, Pritchard and Binding, 1992), on the other hand, consider a lower region of length L1 with emissive power E1 ¼ Emax for a given fuel, and an upper region of length L2 ¼ Lf – L1 (where Lf is the length of the complete flame) with average emissive power E2, where E2 < E1 due to the smoke production. Such models are commonly used to represent the burning of hydrocarbon fuels. Notice that each fuel has a maximum emissive power here denoted by Emax. The solid flame model assumes that the flame is represented by a solid cylinder of diameter Df which extends upwards with length Lf: Wind causes distortions in the flame geometry. As shown in Fig. 2, an inclined flame occurs due to wind, thus adding new variables to repre­ sent flames: Hf is the height reached in elevation; ΔD is the flame displacement sideways; ϕ is the angle of flame inclination; and Hs is the depression of the flame measured downwards from the edge of the tank. This paper focuses on a two-tank configuration, both tanks having a diameter D and height H, but the source tank is open at the top while the target tank has a fixed conical roof. The fuel stored in both tanks is assumed to be gasoline. The flame may be located at the top or at the base of the source tank, whereas different scenarios of gasoline level are considered at the target tank. Additionally, the influence of the

separation between tanks and their dimensions are also evaluated. To perform computations, two specific tank dimensions are consid­ ered: D ¼ 11.44 m and D ¼ 17.16 m, having both an aspect ratio H/ D ¼ 1. Based on minimum separations specified by international regu­ lations, four values of separation d between tank walls are considered: d ¼ 0.33D, d ¼ 1.0D, d ¼ 1.5D, and d ¼ 2.0D. The assumed environ­ mental conditions are the ambient temperature Ta ¼ 20 � C; relative humidity 40%; and five wind speed scenarios are investigated between zero and 45 km/h. Fluid levels zfuel in the target tank have values zfuel ¼ 0, zfuel ¼ 0.5H, and zfuel ¼ 0.95H. Tanks are made of A36 steel. The flame was modeled using a two-layer solid model, and this is the first time this model is used in this context: all previous studies have used a one-layer model. The geometry is given by a vertical cylinder for zero wind speed or an inclined elliptic cylinder with variable tilt angles for the different wind speeds considered. In the absence of wind, the flame diameter was assumed to be the same as in the source tank, i.e. Df ¼ D. Geometric parameters of the flame were estimated using empirical information available in the literature. To simplify the equa­ tions, the non-dimensional velocity of combustion, m*, is defined as m* ¼

m pffiffiffiffiffiffiffiffi

ρo gDf

and

m ¼ m∞ 1

Exp

kβ ​ Df

��

(1)

where ρ0 is ambient density of air; g is gravity. The non-dimensional wind speed given as

Fig. 2. Variables involved in the geometric definition of a flame emerging at roof level in the source tank: a) quiet atmospheric environment, b) under wind conditions. 3

S.N. Espinosa et al.

u* ¼ � Df

u∞

Journal of Loss Prevention in the Process Industries 62 (2019) 103990

efficient combustion, with maximum emissive power; the upper region has a lower value of emissive power due to the presence of smoke or soot. For gasoline, the maximum experimental emissive power ranges between 120 and 170 kW/m2, whereas soot emissivity is around 20 kW/ m2. Estimates were made based on the work of Mudan and Croce (1988) in the form of equations (9) and (10):

(2)

�1=3

g​m

ρo

where u∞ is the wind speed at free-field. Parameters m∞ ¼ 0.55 kg/m2s and kβ ¼ 2.1 were adopted for gasoline based on experiments reported by Babrauskas (1983). Following Thomas (1963) under conditions of zero wind speed, the vertical flame height Hf is assumed in terms of the nondimensional velocity of combustion of fuel, m*, and on the flame diameter Df

E2 ¼ Emax Exp

For the geometry of the flame immersed in a windy environment, Thomas (1963) proposed the following expressions for the flame length, Lf, and the flame height, Hf, where ϕ is the angle of inclination of flame measured with respect to the vertical direction. Lf ¼ 55 ​ Df ​ ðm* Þ

2=3

ðu* Þ

*

0:5

Hf ¼ cos½ϕ�Lf ¼ ðu Þ

(4)

0:21

Fr0:5

and

Hs ¼

ΔD 3

� � � � �

(7)

u∞ Df u2 ; Fr ¼ ∞ v gDf

(8)

and ν is the kinematic viscosity of air, measured in [m2/s]. Based on the assumed dimensions D ¼ H ¼ 11.4 m of the source tank, for wind speed equal to zero (u∞ ¼ 0), the flame geometry is given by Hf ¼ Lf ¼ 17.5 m, with a clear flame region at the bottom L1 ¼ 2.1 m. For wind speed of 45 km/h (or u∞ ¼ 12.5 m/s) the flame inclination is ϕ ¼ 68� whereas the flame height Hf reduces to only 3 m, with total length Lf ¼ 11 m, and L1 ¼ 3.3 m, ΔD ¼ 7 m and depression Hs ¼ 3 m. For the cases considered in this study, the assumed flame parameters are given in Table 1. The radiation emission from the flame surface was next obtained. In the two-layer model, the lower region is characterized by a more Table 1 Geometrical flame parameters for five different wind velocities. u∞ [m/s]

ϕ [degrees]

Hf [m]

Lf [m]

L1 [m]

ΔD [m]

Hs [m]

0 2.3 3.5 7 12.5

0 30 45 60 68

17.5 13.7 10.2 6.2 4.1

17.5 15.8 14.5 12.5 11.1

2.1 2.4 2.6 3 3.3

0 2 2.7 4.5 7

0 0.7 0.9 1.5 2.3

0:12Df

(10)

Radiation exchange between flame, tank, and the environment; Heat conduction through steel; Natural and forced convection, depending on the case; Radiation through air inside the target tank; Liquid gasoline is assumed as opaque to radiation whereas air inside the tank has unit transmissibility.

In a previous work by the authors (Espinosa et al., 2018), a CFD model was solved to understand the transient thermal behavior of the fuel stored in a tank exposed to the flame radiation, to obtain the resulting velocity, pressure, and temperature fields of the natural con­ vection process as a function of time. As a consequence of mixture be­ tween internal streams, the average temperature of the stored fuel increased slowly between 20 � C and 80 � C, depending on the time of exposure to fire. In this work, similar results to those given by the CFD model are obtained by a heat transfer model with natural convection coefficients estimated as a function of gasoline properties and the sur­ face temperature of the tank. The temperature of air inside the target tank was assumed to be constant, with value Ta. Properties of steel, air, and gasoline were computed as a function of temperature. Convection coefficients were estimated in terms of the properties of fuel and the temperatures of the tank surface. The con­ vection coefficients for air and gasoline inside the tank and for air external to the tank were estimated by means of the correlation due to Churchill and Chu (1975) for natural convection or free convection on vertical planes with height H, which may be taken as an approximation for vertical cylinders provided the thickness of the thermal boundary layer is much smaller than the diameter of the cylinder (Incropera and DeWitt, 2002). The film coefficient h and the thermal diffusivity α are given in terms of thermal conductivity K; density ρ; and specific heat at constant pressure cp:

where Reynolds number Re, and Froude number Fr, are given by Re ¼

Exp

��

The heat transfer process from the flame to the target tank depends on an energy balance involving the incident radiation and the energy exchanged between the metal surface of the target tank with the internal fluid (both air and fuel) and with the external fluid (air). Previous works in this field accounted mostly for incident radiation or assumed an empty tank (da Silva Santos and Landesmann, 2014; Pantousa, 2018). A detailed heat transfer analysis is performed in this work, by including:

where NC and NH are the number of carbon and hydrogen atoms present in the fuel. The American Gas Association recommends estimating the flame displacement at the base and the depression as a function of the flame diameter Df, and of Reynolds and Froude numbers (SFPE Handbook, 1995): 0:25

0:12Df þ Esoot 1

�

3.1. Energy balance

The length L1 of the lower clear flame depends on the type of burning fuel, the flame diameter, and wind speed. Smoke production is directly proportional to the ratio between carbon and hydrogen atoms in the fuel, and increases with the pool diameter because access of air to the pool center becomes more difficult, thus reducing the combustion ve­ locity. The opposite effect occurs if wind speed increases. Such aspects are considered using a correlation due to Pritchard and Binding (1992) given by � � 2:49 NC L1 ¼ 11:404 ​ ðm* Þ1:13 ðu* Þ0:179 Df (6) NH

ΔD ¼ 28:68 ​ Df ​ Re

�

3. Heat transfer from fire source to target tank

(5)

Lf

�

where E1 and E2 correspond to clear flame and smoky flame, respec­ tively. To carry out the computations, a maximum emissive power Emax ¼ 140 kW/m2 was adopted for gasoline, and Esoot ¼ 20 kW/m2. Notice that eqs. (9) and (10) are different from those used by da Silva Santos and Landesmann (2014) because they used a single layer model with a single emissive power for the complete flame.

(3)

Hf ¼ 42 ​ Df ðm* Þ0:61

(9)

E1 ¼ Emax

h ¼ NuH ​

K ; H

α¼

K

ρ cp

(11)

For a given fluid, the non-dimensional numbers of Rayleigh, Prandt, and Nusselt (average) are, respectively 4

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

where the non-dimensional coefficient for thermal expansion is β; ν denotes kinematic viscosity ν ¼ μ/ρ; Ts is the temperature of the metal surface; and T∞ is the temperature of the fluid in free flow. The fuel properties are computed at film temperature Tfilm Tfilm ¼

Ts þ T∞ 2

3.2. Finite element model The main result of the present study is the stationary temperature field on the walls of the cylinder and the roof in the target tank. This is obtained from the heat transfer analysis due to radiation between flame, target tank and environment; heat conduction through the walls and roof of the target tank; convection between the surfaces and the fluid in contact; and radiation exchange through air inside the target tank. The general-purpose finite element code ABAQUS (2006) was used in this work to carry out the thermal simulation of heat transfer from source to target tank. Discretization of the domain was achieved using DS6 six-node triangular elements for the conical roof, and DS8 eight-node quadratic elements for the cylindrical shell. The discretization covers the flame at the source tank and the target tank, with a separation values d between them. The cases reported in this work were computed for four different values of d. A view of the finite element configuration is shown in Fig. 3, for conditions of wind acting on the flame and also for zero wind speed.

(13)

Because the temperature of the target tank is not known a priori, computation of the film coefficient was performed in an iterative way by taking an average value T∞. For the scenario under wind, the external film coefficient is computed based on correlations obtained for forced convection and cross-flow around cylinders of diameter D. In this case, the relation due to Zhukauskas (1972) was used and an iterative procedure was applied because the properties depend on the film temperature: � NuD ¼ 0:076 ​ Re0:7 Pr0:37 ReD ¼

Pr Prs

�1=4 (14)

u∞ D

3.3. Convergence of the solution

ν

h ¼ NuD ​ K=D

Convergence studies were performed and results are shown for the

, T∞ÞH 3

RaH ¼ gβðTs

, ðν ​ αÞ;

Pr ¼ ν

( ​ α;

NuH ¼ 0:825 þ h

0:387Ra1=6 H 1 þ ð0:492=PrÞ9=16

(15)

Values of ε for A36 steel available in the literature range between 0.3 (for surface without oxidation) and 0.8 (for rusted surfaces). For the external surface of a target tank, a value 0.8 was adopted on account that the surface is smudged by the effect of fire; however, the lower value 0.3 was adopted for the internal surfaces. The atmospheric transmissivity τ (which accounts for radiation attenuation induced by molecules of vapor and CO2 in atmospheric air) was obtained using an estimate due to Wayne (1991) in the form: 0:0117 logXH2 o 0:02368ðlogXH2 o Þ2 0:03188 logXco2 þ 0:00164ðlogXco2 Þ2

τ ¼ 1:006

X H2 o ¼

� 2:8865112 φPsatðTa Þ Ta

Xco2 ¼ 273 d=T

a

(12)

case of separation between flame and tank equal to the diameter D, the target tank filled with fuel up to H/2, and wind speed 45 km/h. In all cases, a dense mesh was adopted at the top of fuel stored in the target tank and at the junction between the cylinder and the roof. Only the front part of the flame was discretized with finite elements. Results of the temperature profile along the meridian most exposed to fire is shown in Fig. 4, and results around the circumference at elevation 11.26 m (where maximum temperatures occur) for four mesh configurations are shown in Fig. 5. Mesh 1 (4073 elements) has elements with 0.5m in the vertical direction and 4.4� in the circumferential di­ rection; Mesh 2 (5225 elements) has elements with 0.25m in the vertical direction and 4.4� in the circumferential direction; Mesh 3 (5425 ele­ ments) has elements with 0.5m in the vertical direction and 2.2� in the circumferential direction; Mesh 4 (6383 elements) has elements with 0.25m in the vertical direction and 2.2� in the circumferential direction. Quadrilateral 8-node elements (identified as DS8 in ABAQUS) and triangular 6-node elements (identified as DS6 in ABAQUS) were used in the discretization of cylindrical surfaces and roof, respectively. The most significant feature in Fig. 4 is the jump in temperatures

The incident radiation on adjacent tanks, q’’f ; in units of energy per unit surface, is estimated by the emissive power of the flame, E, which is modified by the emissivity of the tank surface ε, the view factor Fij (which considers the geometry and relative position of the tanks) and the atmospheric transmissivity τ: q’’f ¼ ετFij E

)2 i8=27

(16) (17) (18)

where Ta is ambient temperature; Psat(Ta) is the water saturation pres­ sure at Ta, measured in [mm] Hg; and φ is the atmospheric relative humidity. Gases are transparent to radiation, while liquids interfere with ra­ diation so that the energy exchange due to internal radiation is modified by the level of fluid stored in the target tank. Evaporation of different components of gasoline has not been considered in this work, so that pure air is assumed on top of the fuel level. Fig. 3. Finite element discretization of source and target tanks, considering (a) zero wind speed, (b) wind speed (tilt of the flame towards the target tank). 5

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

Fig. 4. Temperature distribution along the meridian in target tank facing the flame.

Fig. 6. Finite element mesh used to model the flame and the target tank.

measure radiant heat flux. The main features of these tests were modeled using the present formulation, which was implemented using ABAQUS. The meshes employed elements of size 0.1m � 0.1m for the flame and 0.05m � 0.05m for the target tank. The adopted parameters were the same as used in the computations in the rest of this paper. The tem­ perature at the source was computed using data provided by Mansour on ambient temperature, wind speed and relative moisture. Experimental temperatures are plotted from thermocouples placed in the stored gas­ oline, whereas the present computational curves correspond to tem­ peratures on the steel shell. In a test identified as Test 2, the temperature was recorded in time at three points in the gasoline, at an elevation of 0.25 m from the base of the tank, and results are shown in Fig. 7. The starting (ambient) tem­ perature was close to 16 � C, whereas the initial gasoline temperature was 24 � C. The duration of the test was 20 min, and at a time 11.3 min the gasoline stored in the target tank ignited. The plot in Fig. 7 shows a smooth increase in temperature. In Test 3 (Fig. 8) the same procedure was followed to identify tem­ perature variations in elevation: This was done by thermocouples placed at 0.05 m, 0.125 m, and 0.25 m from the bottom of the target tank. The initial temperature of gasoline stores was 26 � C and the duration of the test was 14 min. Differences were found between the three locations, with higher temperatures recorded at higher levels. The temperature versus time is a smooth curve for 0.05 m and 0.125 m, but a more irregular pattern is found for the 0.25 m thermocouple. At about 10 min from the start of the test, gasoline in the target tank had reached a uniform temperature of 48 � C. The average incident radiant heat at the target tank was measured as 44 kW/m2 in Test 2 and 40 kW/m2 in Test 3. The present heat transfer model estimates the temperatures on the outer surface of the target tank, and not in the stored fuel, as was done in the experiments by Mansour. Notice that there are differences between both measurements because temperatures in steel are higher than those in the stored fuel; but with increasing time, the temperature in gasoline increases up to the values in the steel shell. Furthermore, because the thermal diffusion a ρkc in steel is much higher than in liquid gasoline, then

Fig. 5. Temperature distribution around the circumference in target tank, computed at elevation 11.26 m, and at elevation 3m (seen as a black curve) which is the level in contact with fuel.

associated with the interface between fuel and air inside the target tank, and all meshes capture the details very well. Only minor differences are found among the four meshes shown in the plots. Again, small differ­ ences are shown to occur for results around the circumference. Based on the previous studies, a mesh with 4073 elements on the target tank was used to carry out most computations reported in Section 4. 3.4. Comparison between the present heat transfer model and field tests Field tests were conducted by Mansour in May, 2009, and were re­ ported in Chapter 4 of his doctoral thesis (Mansour, 2012). Three tests were conducted by Mansour, to measure temperatures in the liquid stored in the target tank at various locations, by means of thermocouples. A small steel tank having D ¼ 0.42 m, H ¼ 0.57 m and thickness 1 mm, filled with gasoline up to 0.35m level, was used as the target tank. The tank was place on a small platform at 0.6 m above ground level. The pool fire was ignited in a 2.4 m diameter open cylinder, filled with 1m of water and a 0.05 m layer of fuel. The distance between tanks (shell to shell) was 2 m. A radiometer was placed above the target tank in order to

the shell temperature reaches a steady state faster than the stored fuel. Finally, the temperature estimated in the computations correspond to the steel shell, and because of the high conductive property of steel

6

S.N. Espinosa et al.

Journal of Loss Prevention in the Process Industries 62 (2019) 103990

Fig. 7. Experimental data for Test 2 at an elevation of 0.25m (Mansour, 2012), and results of present model using ABAQUS. Experimental temperatures are plotted from thermocouples in the gasoline, whereas present computational curves correspond to temperatures on the steel shell.

Fig. 8. Experimental temperatures measured in fuel at three different elevations for Test 3 (Mansour, 2012), and results of present model computed on the at the same elevations.

the temperatures tend to become more or less uniform even at different elevations. This is more so in the small-scale model tested by Mansour, in which distances are very small. The present results are consistent with those of Mansour, in the sense that the temperature on the steel shell facing the flame is higher than the temperature in gasoline, and the fuel approaches the shell temperature with time. There are test features not taken into account in the com­ putations with the present heat transfer model, including the possibility of fractional distillation in gasoline that would modify the fuel proper­ ties. Other possible sources of difference may be related to wind effects: Mansour reports that Tests 2 and 3 were done without wind (lower than 1.04 m/s), but his photographs show a flame inclination of about 30� towards the target tank, which would increase the incident radiation.

positions of the flame at the source, five wind speeds (ranging from zero to 45 km/h), and four separations between tanks. The main results from the study are summarized in this section. 4.1. Influence of vertical location of flame To explore the behavior of the target tank under an adjacent fire, consider first the temperature profile along the meridian at θ ¼ 0, where θ is the angle measured with respect to the direction given by the centers of the two tanks, and vertical coordinate z measures distances from ground level upwards. In this section the diameter of both tanks is D ¼ H ¼ 11.44 m, the distance between tanks is d ¼ D, the wind speed is assumed to be zero, and the target tank is empty. For the flame acting from the top of the source tank, the temperature at the base of the target tank is approximately 100 � C; values increase with elevation up to a maximum of 230 � C at the junction between cylinder and roof (2.3 times the temperature at the base). The temper­ atures decrease on the roof to a minimum at the roof center. Considering the circumferential variation, temperatures are maximum at θ ¼ 0,

4. Parameters controlling the response A total of 26 cases were studied in this work, considering two different tank diameters, both having H¼D. The computations were performed based on three levels of fluid stored in the target tank, two 7

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

decrease with a sinusoidal trend between θ ¼ 0 and θ ¼ π /2; and remain constant between θ ¼ π/2 and θ ¼ π . Other authors have taken this scenario into account in their calculations. The actual location of the flame at the source tank was only considered by Liu (2011), and it has a significant impact on the results. In the scenario identified as “fire location at the base” in Fig. 1.b, it is assumed that fire has extended from roof level to ground level, thus increasing the radiation surface and causing a modification of View Factor between solid flame and target tank. At the base of the target tank, the temperature now reaches approximately 350 � C, which is 3.5 times higher than in the case of fire starting at roof level. This value increases moderately with elevation up to more than 400 � C; the maximum is not at the junction with the roof but at an intermediate (1.15 times the value at the base). Values decrease on the roof down to ambient temperature at the back of the tank. It is interesting to compare the present results with those already available in the literature. The results show that a flame radiating from the top of a tank, as considered by da Silva Santos and Landesmann (2014) and Pantousa (2018) has a less significant thermal effect than if it is located at ground level. This is associated with the larger area of ra­ diation present in the latter case that significantly increases the heat radiated by the flame. Further, a flame acting from ground level mod­ ifies the View Factor and a greater fraction of radiation hits the target tank, thus leading to a higher temperature on the shell surface. Liu et al. (2012) examined the influence of several vertical fire locations to conclude that any localization of the flame provides a temperature profile which is between the two extreme cases shown in Fig. 4.

to 237 � C at the top of the empty target tank. If the tank contains fuel, the temperature remains at 82 � C at the zone in contact with fuel. A tran­ sition occurs at an elevation higher than fuel level, and the temperature approaches values in the empty tank. The reason for this decrease in temperature is the cooling effect of the fuel on the steel surface in contact with it: the average convection coefficient of fuel is two orders of magnitude higher than the same coefficient in air, and fuel is opaque to radiation. Fig. 11.b considers the extreme case of fire at ground level. The temperature profiles follow the same patterns as in Fig. 11.a, but with higher values due to the increase in incident radiation. In an empty tank, the temperature on the surface increases from 347 � C at the base to 416 � C at the top of the cylinder, and decreases on the roof where ra­ diation is lower. If the tank contains fuel, the temperature remains almost constant at 116 � C in the region in contact with fuel, and jump towards values in the empty tank at higher elevations. The plots in Fig. 11.a and 11.b allow predicting the temperature profile for other fuel levels because the internal surfaces in contact with air show the same thermal behavior. This effect was originally reported by Liu (2011) for a flame at ground level and in the absence of wind, but her results yield higher temperatures because the separation considered between tanks is three times lower than values adopted in this work. 4.3. Influence of wind speed In the previous section, the effect of wind was not taken into account. It is assumed in this section that wind blows tilting the flame towards the target tank, which is the worst scenario. This causes that the flame be­ comes closer to the target tank and thus maximizes the influence of fire by increasing the net radiation incident on the walls of cylinder and roof. Depending on the separation between tanks, the inclination may lead the flame to touch a neighbor tank, so that a secondary flame develops (Cozzani et al., 2006). Previous studies in this topic were presented by da Silva Santos and Landesmann (2014) and Pantousa (2018), who both assumed a wind speed of 5 m/s. The influence of increasing wind velocity on the temperature dis­ tribution in the target tank is evaluated. The study covers a range of velocity between 0 and 12.5 m/s (45 km/h), with angle of inclination between 0� and 68� , respectively. Intermediate velocities were also considered to cause flame inclinations of 30� , 45� , and 60� . The flame parameters considered are shown in Table 1. Temperatures in elevation and around the circumference are shown in Figs. 12 and 13 for an empty tank, two extreme flame positions at the source tank and one diameter separation between tanks. For a flame located at the top of a tank, Fig. 12.a, wind has the effect of increasing the slope of the temperature profile, with temperatures from 100 � C to 250 � C at the base and reaching close to 500 � C at the top of the target tank. Such variations are associated to the flame inclination towards the tank as wind speed increases, and is being taken into ac­ count by the View Factor that affects the incident radiation. However, when the flame extends to the complete source tank, the increase in incident radiation at the base of the target tank is larger than the effect of wind, and the differences in temperatures in the five cases investigated is less than 50 � C. Of course, wind effects are more important at the top, with the consequence that temperatures there are higher than those shown in Fig. 12.a, with temperatures higher than 500 � C for wind of 45 km/h. The maximum temperatures are reached in the meridian which is closest to the flame. Such temperatures are compared in Fig. 14 for two extreme positions of the flame as a function of wind speed, and in each case the maximum occurs at different elevations. This can be seen in Fig. 13, which shows the circumferential variation of temperatures on the target tank, at four elevations close to the top of the cylindrical shell. In all cases the maximum temperatures occur at the meridian with θ ¼ 0 (the shortest distance to the flame) and then decrease following a si­ nusoidal curve; minimum values are computed at the region with 90� <

4.2. Influence of the level of fuel stored in the target tank The incidence of fluid level stored in the target tank was originally investigated by Liu (2011). Fig. 10 shows the three level of fuel considered in this work into the target tank. The corresponding results are reported in this section for zero wind velocity and for two flame positions. The combined wind/fuel level situation is considered in Sec­ tion 4.3. The case for zero wind velocity on an empty tank was already addressed in Fig. 9. The temperature profile for an empty tank is compared in Fig. 6 with those for a target tank having two different fuel levels. The vertical axis in Fig. 11 is non-dimensional by dividing the coordinate z by H, and extends to consider effects on the roof (z/H>1). Temperatures are seen to increase in Fig. 11.a from 97 � C at the base up

Fig. 9. Temperature in the target tank for two flame positions (a) at the top of the source tank; (b) at the bottom of the source tank, for zero wind velocity and empty target tank. 8

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

Fig. 10. Fuel levels considered in this work. a) empty tank, b) fuel filling up to 0.5H, c) fuel filling up to 0.94 H.

Fig. 11. Influence of fluid level in target tank on temperature profile along a meridian in target tank for zero wind speed, separation d ¼ D. (a) Flame from roof level of source tank, (b) Flame from ground level.

Fig. 12. Temperature profile along a meridian in target tank for increased wind speeds, zfuel/H ¼ 0, separation d ¼ D. (a) Flame from roof level of source tank, (b) Flame from ground level.

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

Fig. 13. Circumferential variation of temperatures at elevations 0.7H, 0.8H, 0.9H and 1.0H, for two wind conditions (u ¼ 0 and u ¼ 45 km/h). Flame from top of the source tank and fuel level zfuel/H < 0.6.

Fig. 16. Influence of average temperature of fuel stored in the target tank, for 45 km/h wind and zfuel/H¼ 0.5.

θ < 180� . Values at wind speed u ¼ 45 km/h are considerably higher than those obtained for zero wind velocity. The combined effect of wind and fuel level is shown in Fig. 15, and it is again characterized by the limiting cases of empty and full tank conditions. The patterns of temperature in the meridional direction are similar to what was previously shown for cases without wind, as shown in Fig. 11. Comparisons between empty tanks and those with fuel are shown in Fig. 15: the maximum temperatures are reached between the fuel and the roof, and a sharp transition is seen at fuel level. If the flame extends from ground level, then higher temperatures are reached. For other fuel levels the pattern can be estimated based on Fig. 15.a and 15. b. 4.4. Influence of temperature of fuel stored in the target tank The only case in which the temperature of a fuel stored was included in an analysis was reported by Liu (2011), for a fixed value of 100 � C. It is expected that the temperature of the fluid stored in the target tank should modify the temperature field on the tank walls caused by an adjacent fire. To investigate this effect, two temperatures were consid­ ered in this section, namely 20 � C (ambient temperature), and 80 � C.

Fig. 14. Maximum temperatures on empty target tank for different wind speed. The separation between tanks is d¼D.

Fig. 15. Influence of wind speed on the temperature profile when three different fuel levels are considered and the separation between tanks is d ¼ D. (a) For flame at roof level, (b) For flame at ground level. 10

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

Fig. 17. Influence of separation d between source and target tanks: (a) d ¼ 0.33D; (b) d ¼ 2D. D¼11.44 m, zfuel/H¼0, flame at ground level, zero wind speed.

have been plotted in Fig. 18(a), and they reach Tmax ¼ 637 � C for the short distance d ¼ 0.33D; whereas for intermediate separation d ¼ 1.0D, Tmax ¼ 416 � C; for d ¼ 1.5D then Tmax ¼ 325 � C; and for d ¼ 2D the peak temperature is Tmax ¼ 256 � C. Different criteria have been used to establish safe separation dis­ tances between tanks, or minimum distances to avoid the possibility of extending a fire to neighboring tanks and eventually to the refinery or facility. A temperature-based criterion of autoignition was adopted by Da Silva Santos and Landesmann (2014) and by Pantousa (2018), which for gasoline leads to a temperature of 299� C; thus, only the separation 2D would be a safe condition. However, even if this temperature is reached, a combustion reaction will not occur if the composition of vapors is not within the flammability range of the fuel. On the other hand, in cone roof tanks an inert blanketing system is a mandatory requirement to avoid the formation of flammable mixtures in the confined volume above the liquid level (NFPA 69, 2008). An alternative criterion was employed by Sengupta et al. (2011) and Abbassi et al. (2014), who established minimum safe designs based on a maximum radiation flux of qrad ¼ 4732 W/m2; it is assumed that fuels receiving radiations lower than that limit will not burn. However,

Fig. 16 shows results for wind speed 45 km/h, for a flame at roof level in the source tank and fuel filling up to zfuel ¼ 0.5H. The temperature profiles are only modified in the region in contact with fuel, but remain the same in the region in contact with air. The increase in temperature at the base, as a consequence of an increase in fuel temperature, is more than 100%. 4.5. Influence of the distance between tanks It is intuitive to think that tanks close to each other yield higher temperatures in the target tank than if they are further apart; but quantification of this influence can only be achieved by numerical ex­ periments. To investigate the effect of distance d between source and target tanks (shell to shell distance), this research started by considering the reference case of a flame at ground level, empty target tank, and zero wind speed. Temperature distributions on the target tank are shown in Fig. 17 for two separations, d ¼ 0.33D and d ¼ 2D. The first case corresponds to the minimum distance established according to SFPE (1995), whereas the second case is a more conservative design. Similar patterns were ob­ tained by Liu (2011) for D¼20m, H ¼ 40 m and d¼0.33D. The temperature profile in elevation together with the peak values

Fig. 19. Separation between tanks for fire impingement, as a function of wind speed. The top region of the plot represents configurations for which fire impingement will not occur.

Fig. 18. Influence of separation d between source and target tanks on tem­ perature. Flame at ground level, zfuel/H ¼ 0. zero wind speed. 11

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Journal of Loss Prevention in the Process Industries 62 (2019) 103990

to represent the heat transfer processes from a flame to an adjacent tank. The main original contribution of this work concerns the evaluation of heat exchange at the target tank using an energy balance that includes not just radiation but also convection and radiation to internal and external fluids. An energy balance was established based on the emissive power from the flame caused by burning fuel stored in the source tank; this allows evaluation of the temperature field on the target tank. Computations were carried out with the help of a general-purpose finite element code using a heat transfer module. Results were restricted to atmospheric tanks storing gasoline and quantitative differences would be obtained for other fuels, but the same qualitative behavior is expected to occur. Various parameters have been considered in the analyses, and the main results may be summarized as follows: � For the situation in which the flame burns from the top of the cyl­ inder in the source tank, and for a one diameter separation between tanks, temperatures on the target tank for zero wind speed are in the order of 250 � C, with values increasing from base to roof level. Temperatures considerably decrease on the conical roof to a mini­ mum on the part of the tank not facing fire. � The actual location of the flame plays a significant role: For a flame starting at the base of the source tank, temperatures on the target tank increase by a factor of three, reaching maximum values in the order of 400 � C. � In both cases, flame at roof level and at ground level, the presence of fuel stored in the target tank has a cooling effect, with the conse­ quence that the temperatures on the shell wall in contact with fluid remain almost constant in elevation, while for the top part of the tank the temperatures reach the same values as in an empty tank. There is a localized jump between the two bounding temperature distribu­ tions: A lower bound to temperatures is given by the full tank whereas an upper bound is given by the empty tank. � Wind has an important influence on temperatures. For a flame at the top of the source tank with a wind speed of 45 km/h, temperatures at the top increase by a factor of two. This influence is not so remarked for a flame at ground level, with an increase factor of less than 1.5. Because wind causes an inclination of the flame, the roof tempera­ tures also increase, reaching values higher than in the cylinder. � Assuming a given slenderness ratio H/D, the size of a tank does not significantly modify the temperatures in the target tank. � The distance between flame and tank, on the other hand, signifi­ cantly modifies the temperatures and is a key factor to consider in order to estimate possible domino effects in a tank farm. The results show that separation of 1/3 the diameter of the tank should not be recommended in areas where winds of 20 Km/h are likely to occur.

Fig. 20. Influence of tank size on temperatures, for d ¼ 1.0D to d ¼ 2.0D considering an empty target tank, with zero wind speed and flame from ground level.

Cozzani et al. (2006) published a set of values available in the literature with limits of radiation for tanks between 9500 W/m2 and 38, 000 W/m2. Such variation in maximum radiation is associated with variables affecting safe distances between tanks, including type and volume of stored fuel, tank dimensions, duration of the accident, and atmospheric conditions, so that it is not possible to establish a simple general criterion. On the other hand, in an analysis in which fire effects are scaled not only the incident radiation intensity needs to be consid­ ered but also the possibility of fire impingement between flame and neighboring tanks (Cozzani et al., 2006). Wind reduces the effective distance between tanks, so that it is important to estimate the separation that allows fire impingement under increasing wind velocities. This is shown in Fig. 19, showing relative distance d/D that allows direct con­ tact flame/tank for different wind speed. In regions with high winds the minimum safe distances to avoid direct fire contact are higher, and recommendations of d/H ¼ 0.3 can only be used if the expected wind speed is less than 20 km/h. 4.6. Influence of tank size The studies reported in previous sections correspond to given di­ mensions of a specific case. However, one may question the validity of such results for other dimensions, even when the relative geometries remain the same. To investigate this effect, the same case of tanks having H/D ¼ 1 has been studied but for larger values of diameter and height of the tanks. Consider new dimensions with a 50% increase in diameter, i.e. D ¼ H ¼ 1.5 � 11.44 m ¼ 17.16 m, and with separations of d ¼ 0.33D, 1D, 1.5D y 2D between tanks, for an empty target tank and zero wind speed. Temperatures along the hottest meridian in two target tanks are compared in Fig. 20, for D¼17.16m and D¼11.44m. To facilitate com­ parison between results, the meridional coordinate has been normalized with respect to H. The same trends are obtained for both tanks di­ mensions and temperature profiles are only marginally affected by the change in dimensions. The conclusion of this section indicates that tank size is not an important parameter in the determination of temperatures or heat flow reaching the target tank, provided the ratio H/D is preserved.

It is believed that the summarized studies of the previous sections have isolated the most significant parameters affecting changes in temperature fields in tanks in the neighborhood of fire. The information provided in this paper may be used in various ways; the authors are specifically interested in its application to the construction of vulnera­ bility or fragility curves, but for these to be achieved, the structural analysis of the target tanks should be carried out. Finally, the present computational study is based on a heat transfer model of the radiation effects from the flame to the target tank. This approach has also been used by most previous authors in this field, but there are other possibilities not explored in these works, and the main one is a Computational Fluid Dynamics (CFD) approach. CFD method may have advantages over the finite element method in modeling fluid flow and heat transfer, especially for modeling radiative heat transfer. This has been discussed by Landucci et al. (2013), among others, but further computational research would be needed before a change in paradigm in modeling this problem occurs.

5. Conclusions An improved computer-based model has been employed in this work 12

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Declaration of competing interest

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The authors declare that there is no conflict of interest in this paper. All funding sources have been listed, the work is our own work, and the paper has not been submitted to any other journal or conference. Acknowledgements Support for this research has been provided by the Science and Technology Research Council of Argentina, CONICET, by a grant to IDIT on “Vulnerability of infrastructure and physical media associated with fuel storage and transportation”. References ABAQUS, 2006. Simulia. Unified FEA. Dassault Systems. Warwick, RI, USA. Abbassi, M., Benhelal, E., Ahmad, A., 2014. Designing an optimal safe layout for a fuel storage tanks farm: case study of Jaipur oil depot. Int. J. of Chemical, Nuclear, Metallurgical and Materials Engineering 2, 157–165. API 650, 2010. Welded Steel Tanks for Oil Storage. American Petroleum Institute, Washington, DC, USA. Babrauskas, V., 1983. Estimating large pool fire burning rates. Fire Technol. 19, 251–261. Batista-Abreu, J., Godoy, L.A., 2011. Investigaci� on de causas de explosiones en una planta de almacenamiento de combustible en Puerto Rico, Revista Internacional de Desastres Naturales. Accidentes e Infraestructura Civil 11 (2), 109–122. Batista-Abreu, J., Godoy, L.A., 2013. Thermal buckling behavior of open cylindrical oil storage tanks under fire. ASCE J. Performance of Constructed Facilities 27 (1), 89–97. Beyler, C.L., 2002. Fire hazard calculations for large, open hydrocarbon fires, third ed. In: SFPE Handbook of Fire Protection Engineering. National Fire Protection Association, Quincy, MA, pp. 3.268–3.314. Buncefield Major Incident Investigation Board, 2008. The Buncefield Incident, 11 December 2005, Final Report. The Office of Public Sector Information, Richmond, Surrey, UK. Chang, J.I., Lin, Ch-C., 2006. A study of storage tank accidents. J. Loss Prev. Process. Ind. 19, 51–59. Churchill, S.W., Chu, H.H.S., 1975. Correlating equation for laminar and turbulent free convection from a vertical plate. Int. J. Heat Mass Transf. 18, 1323. Considine, M., 1984. Thermal Radiation Hazard Ranges from Large Hydrocarbon Pool Fires. Safety & Reliability Directorate, UK Atomic Energy Authority, Culham, Oxfordshire, UK. Cozzani, V., Gubinelli, G., Salzano, E., 2006. Escalation thresholds in the assessment of domino accidental events. J. Hazard Mater. A129, 1–21. Da Silva Santos, F., Landesmann, A., 2014. Thermal performance-based analysis of minimum safe distances between fuel storage tanks exposed to fire. Fire Saf. J. 69, 57–68. Espinosa, S.N., Jaca, R.C., Godoy, L.A., 2018. Thermal and structural analysis of a fuel storage tank under an adjacent pool fire. Fire Research 2 (1), 31–36.

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